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Title: Quantum solution for the one-dimensional Coulomb problem

Abstract

The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct--such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is not its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.

Authors:
; ;  [1];  [2];  [2]
  1. Departamento de Fisica, Universidad Autonoma Metropolitana, Unidad Iztapalapa, Apartado Postal 55-534, Iztapalapa CP 09340 D. F. (Mexico)
  2. (Mexico)
Publication Date:
OSTI Identifier:
21550229
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 83; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.83.064101; (c) 2011 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BINDING ENERGY; COULOMB FIELD; EIGENFUNCTIONS; EIGENSTATES; HYDROGEN; MATHEMATICAL SOLUTIONS; ONE-DIMENSIONAL CALCULATIONS; QUANTUM MECHANICS; SINGULARITY; SUPERSELECTION RULES; SUPERSYMMETRY; ELECTRIC FIELDS; ELEMENTS; ENERGY; FUNCTIONS; MECHANICS; NONMETALS; SELECTION RULES; SYMMETRY

Citation Formats

Nunez-Yepez, H. N., Salas-Brito, A. L., Solis, Didier A., Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Apartado Postal 21-267, Coyoacan CP 04000 D. F., and Facultad de Matematicas, Universidad Autonoma de Yucatan, Periferico Norte Tablaje C. 13615, Merida, Yucatan. Quantum solution for the one-dimensional Coulomb problem. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.064101.
Nunez-Yepez, H. N., Salas-Brito, A. L., Solis, Didier A., Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Apartado Postal 21-267, Coyoacan CP 04000 D. F., & Facultad de Matematicas, Universidad Autonoma de Yucatan, Periferico Norte Tablaje C. 13615, Merida, Yucatan. Quantum solution for the one-dimensional Coulomb problem. United States. doi:10.1103/PHYSREVA.83.064101.
Nunez-Yepez, H. N., Salas-Brito, A. L., Solis, Didier A., Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Apartado Postal 21-267, Coyoacan CP 04000 D. F., and Facultad de Matematicas, Universidad Autonoma de Yucatan, Periferico Norte Tablaje C. 13615, Merida, Yucatan. 2011. "Quantum solution for the one-dimensional Coulomb problem". United States. doi:10.1103/PHYSREVA.83.064101.
@article{osti_21550229,
title = {Quantum solution for the one-dimensional Coulomb problem},
author = {Nunez-Yepez, H. N. and Salas-Brito, A. L. and Solis, Didier A. and Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Apartado Postal 21-267, Coyoacan CP 04000 D. F. and Facultad de Matematicas, Universidad Autonoma de Yucatan, Periferico Norte Tablaje C. 13615, Merida, Yucatan},
abstractNote = {The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct--such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is not its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.},
doi = {10.1103/PHYSREVA.83.064101},
journal = {Physical Review. A},
number = 6,
volume = 83,
place = {United States},
year = 2011,
month = 6
}
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